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This section presents efficiency scores when the level of farm debt is fixed. In this case, the level of debt, which is an approximation for the farm’s capital availability, is regarded as a fixed input because it cannot be adjusted by the operator. Conceptually, this variable is similar to capturing and accounting for uncontrollable factors such as farm soil quality in the production process. As explained in Chapter 3, non-discretionary DEA models account for the direct effect on efficiencies of factors beyond the control of the operator. The level of total debt was used in this way to capture the direct effects of farm capital availability on production. The modified DEA model allows a reference farm to be compared in terms of their outputs, inputs, input prices to those farms that have a smaller or equal level of debt as the reference farm. Debt constrained farms can be thought of as not being able to achieve their potential due to their shortcoming in capital availability33.

Table 5.2 provides summary statistics for the efficiency scores when the level of farm debt was fixed. Technical, allocative, scale and overall efficiencies and inefficiencies for the sample farms are listed for the two models, the basic and the debt-constrained model. The mean values for all farms all years revealed that on average, efficiency scores for the debt-constrained model were larger than those from the basic model. With the debt-constrained model, technical, allocative and scale efficiencies had mean values of 92%, 82%, and 89%, respectively. Each of the efficiencies had a mean which was 2% larger than the basic model. The average overall efficiency score under the debt-constrained model was 68%; which was 5% larger than the average overall efficiency score for the basic model.

33 _{Specifically, the efficiencies under study correspond to the farm efficiencies scores obtained through the Non-}

discretionary DEA model or Debt-constrained DEA model. The farm efficiencies in these models were calculated as in the same way the basic DEA model. There were seven (discretionary) inputs and three outputs; however, this model was modified by adding the constrained that the farms were compared only to corresponding farms with the same or less level of debt. As pointed out before, the resulting the Debt-constrained model rendered farm

efficiencies which were compared not only in terms of the discretionary inputs, but also in terms of their level of debt.

Table 5.2 Summary Statistics of Debt-Constrained Models for 456 Kansas Farms from 1988 to 2007

Model Mean Std. Dev. Minimum Maximum

Basic Inefficiency Scores

Technical 0.10 0.14 0 0.69

Allocative 0.20 0.13 0 0.83

Scale 0.13 0.15 0 0.94

Overall 0.37 0.19 0 0.99

Debt-Constrained Inefficiency Scores

Technical 0.08 0.13 0 0.69

Allocative 0.18 0.13 0 0.74

Scale 0.11 0.14 0 0.96

Overall 0.32 0.20 0 0.99

Basic Efficiency Scores

Technical 0.90 0.14 0.31 1

Allocative 0.80 0.13 0.17 1

Scale 0.87 0.15 0.06 1

Overall 0.63 0.19 0.01 1

Debt-Constrained Efficiency Scores

Technical 0.92 0.13 0.31 1

Allocative 0.82 0.13 0.26 1

Scale 0.89 0.14 0.04 1

For technical and overall efficiencies, these results are expected because of mathematical properties of the two linear programming problems from which the efficiencies are calculated. Compared to the basic models (see Table 5.1), the debt-constrained models (Table 5.2) impose an additional constraint requiring the farm under analysis to be compared to a “virtual reference farm” with the same or less debt. Otherwise the models are equivalent. Because both problems are minimization problems, the debt constrained problem must produce an objective value that is greater than that from the basic model. If the debt constraint does not bind, the solutions to the two types of problems are identical (by definition a non-binding constraint has no effect on the solution). If it does bind, this means the constraint is limiting the objective from reaching its previously low level. While TE and CE scores can only stay the same or increase, AE and SE may move in either direction because they are calculated as ratios of the TE and CE scores. To illustrate, note that AE can be calculated as AE = CE/TE. If, for example, adding debt

constraints to the models caused a farm’s TE score to increase while leaving CE unchanged, its debt-constrained AE score would decrease. The opposite would be true if the farm’s TE score was unaffected while its CE score increased.

Table 5.2 also contains the average inefficiency scores for the sample for each model. The average sample inefficiencies for the basic model were larger than the ones for the debt- constrained model, imposed by the definition of inefficiencies as unity minus the farm efficiency score. The maximum values of inefficiencies were the same in both models for technical and scale efficiency; the maximum value for allocative inefficiency was larger in the basic model than in the debt-constrained one, however, it was the contrary for scale inefficiency.

Table 5.3 Summary Statistics of the Impact of Level of Debt on Efficiencies for 456 Kansas Farms from 1988 to 2007

Efficiency Impact Observations Mean Std. Dev. Minimum Maximum

Technical Positive 877 0.09 0.09 0.01 0.48

Negative 0

No Difference 3,683

Allocative Positive 1,590 0.07 0.09 2E-05 0.60

Negative 464 -0.03 0.04 -0.27 -1E-07

No Difference 2,506

Scale Positive 1,435 0.06 0.08 6E-08 0.56

Negative 811 -0.03 0.05 -0.45 -2E-05

No Difference 2,314

Overall Positive 2,002 0.10 0.11 6E-08 0.64

Negative 0

Table 5.3 divides the sample into 3 groups for each efficiency measure: observations whose efficiency score increased under the debt-constrained model compared to the basic model, observations for which the debt-constrained efficiency score was lower than that under the basic model, and those for which the efficiency scores were the same in both models. The mean and other statistics in this table refer to the observed difference between efficiency scores according to the direction of the change. As discussed above, a farm’s technical efficiency score from the debt constrained model can only be larger or identical to the score from the basic model. The mean technical efficiency score among the debt-constrained group (i.e., observations where the efficiency score rose) was 80%. The average increase in technical efficiency in this group was 9%. The mean technical efficiency for the unconstrained group (81% of the sample) was 92%. The difference in means across groups was statistically significant, implying that although constrained farms had higher technical efficiency scores when they are compared to farms with similar or worse debt levels, they still do not perform as well as unconstrained farms.

A similar story applies to overall efficiency. Again, mathematically, these scores can only increase or stay the same. The mean efficiency of constrained farms was 62%, while the mean efficiency for unconstrained farms was 63%. The difference between the means was

significant at a 5% level. For constrained farms, their average efficiency score was 10% higher in the debt-constrained model than in the basic model.

In the case of allocative and scale efficiency, observations changed positively, negatively, and not at all. With respect to allocative efficiency, most observations were not constrained (55%); their mean allocative efficiency was 81%. 35% of observations were positively constrained in their allocative efficiencies; these observations’ mean technical efficiency was 77%. Only 10% of the observations decreased their basic allocative scores; the average debt- constrained allocative efficiency for this group was 78%. Comparing scale efficiency scores between the debt-constrained model and the basic one gave these results: unconstrained farms had a mean scale efficiency of 87%, positively constrained farms had a mean scale efficiency of 84%, and negatively constrained farms had a mean scale efficiency of 89%. The difference in mean scale efficiencies between the latter two groups was statistically significant.

In general, Table 5.3 shows that for most efficiencies, except for scale efficiency, the farms that were not constrained by debt scored higher than the farms that were constrained. In the case of scale efficiency, negatively constrained farms performed the best. The farms that

were constrained positively, despite the increase in efficiency accounted by the level of farm debt, scored lower than farms that were negatively constrained and their scored had decreased.

Farms in the sample showed that around 50% of all farms were debt-constrained, and thus they underutilized their level of debt relative to their optimal cost-efficient level or over utilized it. Farms constrained in the technical efficiency debt-constrained DEA model showed very low levels of the debt-to-asset ratio, around 0.10. Comparatively, unconstrained farms in the technical efficiency DEA model had a mean debt-to-asset ratio of .31. Such a gap in debt-to asset ratios suggests constrained farms were not using all their capital possibilities, maybe due to risk- aversion or price-uncertainty. Consistently, for all efficiencies reported in Table 5.3, non-debt constrained farms had a debt-to-asset ratio around 0.35; whereas constrained farms had a debt-to- asset ratio around 0.012.